Contact formation on n-type silicon, especially using a high-temperature process, has been the subject of research for more than 40 years. After its application in microelectronics, n-type silicon is widely used in silicon solar cells as the emitter layer. The formation of a low ohmic contact grid using an industrially feasible process step is one of the key features required to improve the solar-cell efficiency. The contact materials, typically deposited in a printing step, have to fulfil several functions: opening the dielectric antireflection layer and forming an intimate metal-semiconductor contact with good mechanical adhesion and low specific contact resistance. As the used contact inks typically contain several functional materials, such as silver and a glass frit, the detailed contact formation is still not entirely understood. Therefore, the chemical reactions during the contact firing process have been studied in detail by thermogravimetric differential thermal analysis in combination with mass spectroscopy. Based on these studies, a contact ink has been developed, optimized and tested on silicon solar cells. In this paper, the mechanism of the etching process, the opening of a dielectric layer, the influence of different atmospheres and the impact of the glass-frit content are investigated. The observed microscopic contact structure, the resulting electrical solar-cell parameters and the studied reactions are combined to clarify the physics behind the high-temperature contact formation.